From PEOPLE Magazine Click to enlarge
Pink has delivered pitch-perfect performances while suspended upside-down from the rafters-and she hoped giving birth to her first child would be another exquisitely choreographed experience. "I was really looking forward to the whole rite of passage-giving birth perfectly present, unmedicated, in the way nature intended," explains the singer, 31, who spent months planning a home birth with midwives. But when she went into labor, her baby was in a frank-breech (head up, piked legs) position and couldn't be flipped, so she ended up having a C-section at the hospital. "Turns out this little girl had other plans," says the renegade pop star. "She is my daughter after all."

Since arriving on June 2, Willow Sage has been causing anything but trouble for Pink (born Alecia Moore) and her motocross-champ husband, Carey Hart, 35. "Everyone gives you this terrifying picture of no sleep at all, bickering," says the Grammy winner. "They make it sound like waterboarding. It's not that bad." Though she admits to "one major meltdown" their first night home: "Carey couldn't figure out who to comfort first. It was pretty funny, actually. Poor guy."

Caring for the baby has been a team effort: Hart gets up with his wife for feedings, and after Pink breast-feeds, he changes and burps Willow, then lets her fall asleep on his chest. "I knew when I met him he'd be a great father, but watching him fall in love, watching him nurture her, I've never been so in love with him in my life," says Pink, who wed Hart in 2006. "He keeps thanking me for giving her to him. It's a beautiful time."

The athletic, outdoors-loving couple (Hart has been spotted toting Willow in a baby carrier on walks near their Malibu home) looked to nature when it came to choosing their daughter's name. "The willow is my favorite tree," explains Pink. "It's the most flexible tree in nature. It can bend and withstand anything. I love that sentiment. I want that for her." As for her middle name, the singer notes, "Sage is cleansing and sacred. And it sounded great together. It doesn't hurt that her last name is Hart-flexible cleansed heart."

Despite their own free-spirited personalities, the couple are already thinking about setting boundaries for their daughter. "There will be no dating as far as Carey is concerned," says Pink. "He can't even talk about it. It's hilarious." Still, both look forward to taking her "on all of our adventures," including Mom's future tours and Dad's supercross races. (Hart is already on the hunt for noise-blocking earmuffs to protect Willow's developing hearing.) Says Pink: "She is so lucky that she'll have the ability to travel to all the different countries and cultures and see so much."

For now Pink and Hart are relishing spending their first weeks at home with Willow. "You hear people say it all the time, how life changes so drastically," says Pink, who recently tweeted that she's gone from "whiskey, tears and cigarettes" to "snot, tears and the color of poop." But she's not complaining. "You can't possibly grasp how beautiful [life] is until you have your child," she says. "I could sit and watch paint dry as long as she was in my arms."